Problem: The fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees Celsius) is modeled by: $p(x)=-2x^2+40x-72$ Which temperatures will result in no fish (i.e. $0$ population)? Enter the lower temperature first. Lower temperature:
Explanation: There are no fish when $p(x)=0$. $\begin{aligned} p(x)&=0 \\\\ -2x^2+40x-72&=0 \\\\ x^2-20x+36&=0 \\\\ (x-2)(x-18)&=0 \\\\ \swarrow &\searrow \\\\ x-2=0\text{ or }&x-18=0 \\\\ x=2\text{ or }&x=18 \end{aligned}$ In conclusion, these are the temperatures that will result in no fish: Lower temperature: $2$ degrees Celsius Higher temperature: $18$ degrees Celsius